Weak ideal invariance and orders in artinian rings: Corrigendum

extremal orders inside simple artinian rings

the aim of this paper is to study orders over a valuation ring v with arbitrary rank in acentral simple f-algebra q. the relation between all of the orders is explained with a diagram. it is thenshown that inside bezout order, extremal v-orders are precisely semi-hereditary. in the last section, theeffect of henselization on maximal and semi-hereditary orders is examined.

Artinian and Noetherian Rings

Artinian Band Sums of Rings

Band sums of associative rings were introduced by Weissglass in 1973. The main theorem claims that the support of every Artinian band sum of rings is finite. This result is analogous to the well-known theorem on Artinian semigroup rings. 1991 Mathematics subject classification (Amer. Math. Soc): primary 16P20, 16W50; secondary 20M25. Let B be a band, that is, a semigroup consisting of idempoten...

Corrigendum: Algorithmic Enumeration of Ideal Classes for Quaternion Orders

This note corrects a mathematical error in the article “Algorithmic enumeration of ideal classes for quaternion orders” [SIAM J. Comput., 39 (2010), pp. 1714–1747]. DOI. 10.1137/120866063 There is an error in the article [2] by the authors: The proof of Theorem B uses a diameter bound (7.1) of Chung [1], D(G) ≤ ⌈ log(H − 1) log(k/λ) ⌉ , which holds for a k-regular directed graph G of size H wit...

Subrings of Artinian and Noetherian Rings

An easy consequence of this is that a left Noetherian (respectively left Artinian) ring which is finitely generated over its center is right Noetherian (respectively right Artinian). Theorem 1 follows easily from Theorem 2, which gives a partial converse to the following standard fact: IfR C S are rings, and ifQ is an injective R-module, then Hom~(S, Q) is an injective S-module (this follows, f...